Euler Polynomials and the Related Quadrature Rule

abstract:
The use of Euler polynomials and Euler
numbers allows us to construct a quadrature rule similar to the
well-known Euler--MacLaurin quadrature formula, using Euler
(instead of Bernoulli) numbers, and even (instead of odd) order
derivatives of a given function evaluated at the extrema of the
considered interval. An expression of the remainder term and
numerical examples are also given.